Dysfunction in the central nervous system of the neonate is often first identified through seizures. The diffculty in detecting clinical seizures, which involves the observation of physical manifestations characteristic to newborn seizure, has placed greater emphasis on the detection of newborn electroencephalographic (EEG) seizure. The high incidence of newborn seizure has resulted in considerable mortality and morbidity rates in the neonate. Accurate and rapid diagnosis of neonatal seizure is essential for proper treatment and therapy. This has impelled researchers to investigate possible methods for the automatic detection of newborn EEG seizure. This thesis is focused on the development of algorithms for the automatic detection of newborn EEG seizure using adaptive time-frequency signal processing. The assessment of newborn EEG seizure detection algorithms requires large datasets of nonseizure and seizure EEG which are not always readily available and often hard to acquire. This has led to the proposition of realistic models of newborn EEG which can be used to create large datasets for the evaluation and comparison of newborn EEG seizure detection algorithms. In this thesis, we develop two simulation methods which produce synthetic newborn EEG background and seizure. The simulation methods use nonlinear and time-frequency signal processing techniques to allow for the demonstrated nonlinear and nonstationary characteristics of the newborn EEG. Atomic decomposition techniques incorporating redundant time-frequency dictionaries are exciting new signal processing methods which deliver adaptive signal representations or approximations. In this thesis we have investigated two prominent atomic decomposition techniques, matching pursuit and basis pursuit, for their possible use in an automatic seizure detection algorithm. In our investigation, it was shown that matching pursuit generally provided the sparsest (i.e. most compact) approximation for various real and synthetic signals over a wide range of signal approximation levels. For this reason, we chose MP as our preferred atomic decomposition technique for this thesis. A new measure, referred to as structural complexity, which quantifes the level or degree of correlation between signal structures and the decomposition dictionary was proposed. Using the change in structural complexity, a generic method of detecting changes in signal structure was proposed. This detection methodology was then applied to the newborn EEG for the detection of state transition (i.e. nonseizure to seizure state) in the EEG signal. To optimize the seizure detection process, we developed a time-frequency dictionary that is coherent with the newborn EEG seizure state based on the time-frequency analysis of the newborn EEG seizure. It was shown that using the new coherent time-frequency dictionary and the change in structural complexity, we can detect the transition from nonseizure to seizure states in synthetic and real newborn EEG. Repetitive spiking in the EEG is a classic feature of newborn EEG seizure. Therefore, the automatic detection of spikes can be fundamental in the detection of newborn EEG seizure. The capacity of two adaptive time-frequency signal processing techniques to detect spikes was investigated. It was shown that a relationship between the EEG epoch length and the number of repetitive spikes governs the ability of both matching pursuit and adaptive spectrogram in detecting repetitive spikes. However, it was demonstrated that the law was less restrictive forth eadaptive spectrogram and it was shown to outperform matching pursuit in detecting repetitive spikes. The method of adapting the window length associated with the adaptive spectrogram used in this thesis was the maximum correlation criterion. It was observed that for the time instants where signal spikes occurred, the optimal window lengths selected by the maximum correlation criterion were small. Therefore, spike detection directly from the adaptive window optimization method was demonstrated and also shown to outperform matching pursuit. An automatic newborn EEG seizure detection algorithm was proposed based on the detection of repetitive spikes using the adaptive window optimization method. The algorithm shows excellent performance with real EEG data. A comparison of the proposed algorithm with four well documented newborn EEG seizure detection algorithms is provided. The results of the comparison show that the proposed algorithm has significantly better performance than the existing algorithms (i.e. Our proposed algorithm achieved a good detection rate (GDR) of 94% and false detection rate (FDR) of 2.3% compared with the leading algorithm which only produced a GDR of 62% and FDR of 16%). In summary, the novel contribution of this thesis to the fields of time-frequency signal processing and biomedical engineering is the successful development and application of sophisticated algorithms based on adaptive time-frequency signal processing techniques to the solution of automatic newborn EEG seizure detection.